September 30, 2012

Big Question: Equilibrium and Stability

My senior year of high school I took my first economics course. We did a business proposal for opening a new restaurant franchise, and we learned some theory. The theory seemed fairly inane and innocuous. All we did was draw X's, occasionally with a price floor or a price ceiling. What seemed so straightforward to me at the time is perhaps the major postulate of modern economics: the idea that markets help supply and demand meet in the middle, automatically. In this post I want to look a bit more closely at that idea and when and why it may be true.

One of the big ideas in economics is that in markets, supply and demand tend toward equilibrium. Equilibrium is the happy place where buyers and sellers, in aggregate, agree on a price that allows as many people to buy the goods as can be supplied by the sellers. If the amount people will pay for the good changes, or the amount it costs to produce the good changes, that side changes their offered price and then the quantity adjusts appropriately. If people want lots of tulips and are willing to pay more for them, then more people will grow them. Similarly, if clothes become cheaper to produce, suppliers will sell them more cheaply and more people will buy more clothes. We own a lot more t-shirts these days than they did 200 years ago.

This is all common sense; the interesting stuff begins when equilibrium doesn't happen.

Which we will come to in a second. First, it is worth mentioning that equilibrium can happen too much. That is, sometimes it is possible to have "multiple equilibria"--markets may have two (or more) price/quantity combinations that buyers and sellers could end up agreeing too. This happens when the demand or supply curve gets more complicated than the traditional X (for example). Another famous macroeconomic example of multiple equilibria is the (simplified Keynesian) explanation for the Great Depression, where a collapse in demand dragged supply down supply, and the economy stabilized below its potential. Multiple equilibria can happen in markets for individual products as well: think about an expensive hotel in an exclusive resort destination, and then a few years later when the everyone has heard about it and college kids go there for spring break. The product is the same (minus the exclusivity) but now supply and demand have come to rest at a lower price.

Multiple equilibria are important--as the Keynes example shows, they are a factor in justifying major fiscal or monetary stimulus programs--but they are only one issue with the concept of equilibrium. The very idea that an economic system will gravitate toward any price point because of supply and demand forces is often suspect. Economists get around this by exploring "static" snapshots of reality, but even this is difficult because the only data you have is one point on the graph, and it is difficult to extrapolate the entire X from one point: the lines of the X may have different slopes or not be straight lines at all. Economists end up relying on "shocks" that hopefully affect only one side of the demand/supply equation: if the supply side stays constant, for example, it may be possible to see how the demand side of the curve is formed.

Static pictures, however, may fail to capture important dynamics--how the system may change over time because of the way supply and demand interact. This is what claims of equilibrium mean: that supply and demand, sellers and buyers, eventually agree on a price that supplies as many goods or services as can be supplied at the price people can pay for it. And eventually the amount supplied and demanded goes toward this price.

In many markets equilibrium may be a realistic assumption. But in others it may not be. Let's break it down a bit. Why might equilibrium--any equilibrium at all--not be a realistic state of affairs in a market?

We can think of markets with two other types of equilibria: equilibria that are unreachable or that are unsustainable. Unreachable equilibria are blocked for some reason, such as regulation or monopolization. The classic textbook example of an unreachable equilibria is price controls, where laws keep prices from reaching the point at which demand is met by as much supply as can be sustainably produced. Rent controls are a price ceiling, and may result in too little housing being provided--the shortage of housing prevents an equilibrium from being reached.

The idea of unsustainable equilibria is more complicated, because it depends on how supply and demand change and react to each other over time. This process of change and interaction works differently in different markets. One common way that they may fail to interact in a way that creates a sustainable equilibrium is when there is poor information: if price signals function poorly or not at all, suppliers and demanders may not have any way of communicating how much they want. This can happen if buyers do not have a good way of knowing how much a good is worth. Education "markets" are a good example: people buying education know that a good education is valuable but have no realistic way of knowing how valuable it will be, because their future is simply too uncertain.

Another example of unsustainable equilibria is Keynes's well-known idea of "animal spirits". This is slightly different than an information problem because, in markets where animal spirits play a prominent role, supply and demand may be based entirely on irrational emotions and perceptions of economic actors. That is, the problem is not in the imperfect information people have, it is in the imperfect rationality of the people themselves (they may have imperfect information as well, but that is beside the point).

Yet another market attribute that can disrupt the sustainability of an equilibrium is market connectedness: markets rarely exist in isolation, and the supply or demand of one market is often influenced by the supply and demand of other markets. One market may affect another market, and this second market may then affect the first market, either directly or through similar effects in other markets. The use of coal could lead to cheaper power which made the production of coal cheaper, for example.

In some cases linked markets may simply be understood as one market: if the cheaper price of flip-flops drives down the price of shoes, it may make better sense to simply analyze the footwear market overall. But in other cases it makes less intuitive sense to link markets because they do not serve as substitutes or complements to each other--they are only related because there is a finite amount of money in the system and money is fungible. Stuart Ewen, in his excellent critique of the genesis of the modern advertising industry, Captains of Consciousness, gives an example from the early days of industrialization: the demand for consumer products causes people to move to the city and work in factories to produce goods, but some of the goods demanded are demanded because of the move toward urbanization. Ewen writes about the Alpine Sun Lamp, which makes people feel like they are outdoors in the sunshine, which they presumably would have been if they still worked on a farm.

In this case connected markets experienced a kind of feedback loop. However, the connections between markets, or between markets and other social realities (such as politics), may have other impacts that preclude the existence of any meaningful equilibria. One example is the current price of Greek public debt: there is certainly a market "equilibrium" that is reached daily based on daily buying and selling, but this equilibrium is based to such a large degree on political expectations that it has little economic significance. Any equilibrium here only appears to be determined by supply and demand because those are the closest proximate causes. In reality, non-market political occurrences are far more powerful causes of market prices. Another example could be if the prices in a grain market are driven up by speculators searching for safer investments in commodities instead of in volatile currency markets. In such an example equilibrium in a single market may be meaningless, but any attempt to find an equilibrium across multiple markets is simply too complex to make meaningful sense of either (see: how quickly international trade models get hairy).

When thinking about equilibria, we need to make sure we understand that there may be economic forces (that is, incentives for market participants) pushing supply and demand toward an equilibrium, or there may not be. Or those forces could be pushing in several ways depending on other criteria. Or there may be outside forces that completely overpower any intra-market forces. In the words of Polanyi, "in no case can we assume the functioning of market laws unless a self-regulating market is shown to exist."


  1. How do we know a self-regulating market when we see it? If such markets do exist, how do we know when they are in equilibrium given that economies and markets don't have natural stopping points but are constantly in motion?

    It seems that the discussion of economic forces may be a useful way to think about the pressures pushing prices in one direction or another, but it is harder to accept that there is an actual point where those forces precisely balance.

    1. I think part of Polanyi's point is that there is never really a self-regulating market, because even the archetypical libertarian market still presumes government does a few things, and does them well. Or if you have pre-capitalist societies, exchange is governed by reciprocation or other social convention. Or if you have an entrepot trading economy that exists solely to faciliate exchange, you still can't have a market without powerful extra-market forces, like the city guards or maybe the mafia guy who keeps order.

      So it's not so much a question of identifying a self-regulating market as asking what incentives are provided internally in markets and what must necessarily be imposed externally. Maybe another way of phrasing the sustainable equilibrium issue, then, is whether those internal incentives consistently override changes in external incentives.

  2. I like the framework of internal vs. external market incentives, although I'll have to think through it a bit more. From what I can recall, the typical discussion is that prices are the predominant channel for transmitting incentives to market participants, in which case we would have to look to the determinants of the market price to better understand the internal or external incentives guiding the market.

    Somewhat tangentially, I see the question of external regulation leading to the question of market definition. How do we identify the boundaries of the market we wish to regulate, and on what level? For instance, say there is a market for gasoline. Could we consider that a submarket of the broader market for oil, which itself is a submarket of the broader market for energy and so forth? And then could submarkets for gas be something more specific, like filling station nozzles? And of course externally influencing one market likely has knock on effects to markets for complementary or substitute goods. I suppose the inframarginal principal suggests we should target the narrowest effective group we can identify.

    Sorry if this is going a bit astray from the discussion of sustainable equilibria. I guess in my head I see the issue of market definition as connected to the topic because the more interwoven and nested markets are the harder it is for me to think about an equilibrium for a single market in isolation. I'm maybe picturing something like dropping a bucket of dice, where they all end up with an equilibrium side up, but they are influenced by internal factors (shape, weight), each other (bumping on the way down), and external factors (the floor) in reaching that equilibrium.